Polynomial Schauder basis of optimal degree with Jacobi orthogonality

Jürgen Prestin, Jörn Schnieder*

*Korrespondierende/r Autor/-in für diese Arbeit

Abstract

In our paper we construct a polynomial Schauder basis (pα,β,n)n∈N0 of optimal degree with Jacobi orthogonality. A candidate for such a basis is given by the use of some wavelet theoretical methods, which were already successful in the case of Tchebysheff and Legendre orthogonality. To prove that this sequence is in fact a Schauder basis for C [ - 1, 1] and as the main difficulty of the whole proof we show the uniform boundedness of its Lebesgue constants.

OriginalspracheEnglisch
ZeitschriftJournal of Approximation Theory
Jahrgang174
Ausgabenummer1
Seiten (von - bis)65-89
Seitenumfang25
ISSN0021-9045
DOIs
PublikationsstatusVeröffentlicht - 01.08.2013

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